Cash flow matching with risks controlled by buffered probability of exceedance and conditional value-at-risk

Shang, Danjue; Kuzmenko, Viktor; Uryasev, Stan

doi:10.1007/s10479-016-2354-6

Cited by 25 publications

(34 citation statements)

References 8 publications

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“…. The formula (10) was used in [26] as a definitions of bPOE. The following corollary states mathematical properties for upper bPOE, similar to the properties specified in subsections 3.1 and 3.2 for lower bPOE.…”

Section: Upper Bpoe and Lower Bpoementioning

confidence: 99%

“…Denoting p j := P (ω j ) and X j := X(ω j ), we can rewrite the corresponding bPOE Downloaded 05/03/18 to 128.227.137.156. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php Papers [13,11,26] considered several bPOE minimization problems with a finite observed data sample (X 1 , . .…”

Section: 2mentioning

confidence: 99%

“…Paper [1] promotes bPOE estimation for the purposes of environmental engineering and discusses bPOE calculation for finite samples. Paper [26] minimizes bPOE in bond immunization problem.…”

mentioning

confidence: 99%

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Buffered Probability of Exceedance: Mathematical Properties and Optimization

Mafusalov¹,

Uryasev²

2018

SIAM J. Optim.

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This paper studies a probabilistic characteristic called buffered probability of exceedance (bPOE). It is a function of a random variable and a real-valued threshold. By definition, bPOE is the probability of a tail such that the average of this tail equals the threshold. This characteristic is an extension of the so-called buffered failure probability and it is equal to one minus inverse of the conditional value-at-risk (CVaR). bPOE is a quasi-convex function of the random variable w.r.t. the regular addition operation and a concave function w.r.t. the mixture operation; it is a monotonic function of the random variable; it is a strictly decreasing function of the threshold on the interval between the expectation and the essential supremum. The multiplicative inverse of the bPOE is a convex function of the threshold, and a piecewise-linear function in the case of discretely distributed random variable. The paper provides efficient calculation formulas for bPOE. Minimization of bPOE is reduced to a convex program for a convex feasible region and to linear programming for a polyhedral feasible region and discretely distributed random variables. A family of bPOE minimization problems and corresponding CVaR minimization problems share the same set of optimal solutions.

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Section: Upper Bpoe and Lower Bpoementioning

confidence: 99%

Section: 2mentioning

confidence: 99%

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Buffered Probability of Exceedance: Mathematical Properties and Optimization

Mafusalov¹,

Uryasev²

2018

SIAM J. Optim.

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“…While the superquantile has risen in popularity over the past decade, a related characteristic called Buffered Probability of Exceedance (bPOE) has recently been introduced, first by Rockafellar and Royset (2010) in the context of Buffered Failure Probability and then generalized by . This concept has grown in popularity within the risk management community with application in finance, logistics, analysis of natural disasters, statistics, stochastic programming, and machine learning (Shang et al (2018); Uryasev (2014); Davis and Uryasev (2016); ; Norton et al (2017); Norton and Uryasev (2016). Specifically, bPOE is the inverse of the superquantile in the same way that the CDF is the inverse of the quantile.…”

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confidence: 99%

Calculating CVaR and bPOE for common probability distributions with application to portfolio optimization and density estimation

Norton

Khokhlov²,

Uryasev

2019

Ann Oper Res

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Conditional Value-at-Risk (CVaR) and Value-at-Risk (VaR), also called the superquantile and quantile, are frequently used to characterize the tails of probability distribution's and are popular measures of risk in applications where the distribution represents the magnitude of a potential loss. Buffered Probability of Exceedance (bPOE) is a recently introduced characterization of the tail which is the inverse of CVaR, much like the CDF is the inverse of the quantile. These quantities can prove very useful as the basis for a variety of risk-averse parametric engineering approaches. Their use, however, is often made difficult by the lack of well-known closed-form equations for calculating these quantities for commonly used probability distribution's. In this paper, we derive formulas for the superquantile and bPOE for a variety of common univariate probability distribution's. Besides providing a useful collection within a single reference, we use these formulas to incorporate the superquantile and bPOE into parametric procedures. In particular, we consider two: portfolio optimization and density estimation. First, when portfolio returns are assumed to follow particular distribution families, we show that finding the optimal portfolio via minimization of bPOE has advantages over superquantile minimization. We show that, given a fixed threshold, a single portfolio is the minimal bPOE portfolio for an entire class of distribution's simultaneously. Second, we apply our formulas to parametric density estimation and propose the method of superquantile's (MOS), a simple variation of the method of moment's (MM) where moment's are replaced by superquantile's at different confidence levels. With the freedom to select various combinations of confidence levels, MOS allows the user to focus the fitting procedure on different portions of the distribution, such as the tail when fitting heavy-tailed asymmetric data.

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“…;Norton et al (2017); andShang et al (2018). Further, based on one-dimensional minimization representation of the bPOE, studied statistical properties of empirical estimates of the bPOE.…”

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confidence: 99%

Peer-To-Peer Lending: Classification in the Loan Application Process

Wei

Gotoh

Uryasev

2018

Risks

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This paper studies the peer-to-peer lending and loan application processing of LendingClub. We tried to reproduce the existing loan application processing algorithm and find features used in this process. Loan application processing is considered a binary classification problem. We used the area under the ROC curve (AUC) for evaluation of algorithms. Features were transformed with splines for improving the performance of algorithms. We considered three classification algorithms: logistic regression, buffered AUC (bAUC) maximization, and AUC maximization.With only three features, Debt-to-Income Ratio, Employment Length, and Risk Score, we obtained an AUC close to 1. We have done both in-sample and out-of-sample evaluations. The codes for cross-validation and solving problems in a Portfolio Safeguard (PSG) format are in the Appendix. The calculation results with the data and codes are posted on the website and are available for downloading.

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Cash flow matching with risks controlled by buffered probability of exceedance and conditional value-at-risk

Cited by 25 publications

References 8 publications

Buffered Probability of Exceedance: Mathematical Properties and Optimization

Buffered Probability of Exceedance: Mathematical Properties and Optimization

Calculating CVaR and bPOE for common probability distributions with application to portfolio optimization and density estimation

Peer-To-Peer Lending: Classification in the Loan Application Process

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